Danilov, Leonid Ivanovich On the spectrum of a Landau Hamiltonian with a periodic electric potential \(V\in L^p_{\text{loc}}(\mathbb{R}^2)\), \(p>1\). (Russian. English summary) Zbl 07312112 Izv. Inst. Mat. Inform., Udmurt. Gos. Univ. 55, 42-59 (2020). MSC: 35P05 35J10 PDF BibTeX XML Cite \textit{L. I. Danilov}, Izv. Inst. Mat. Inform., Udmurt. Gos. Univ. 55, 42--59 (2020; Zbl 07312112) Full Text: DOI MNR
Danilov, L. I. Spectrum of the Landau Hamiltonian with a periodic electric potential. (English. Russian original) Zbl 1445.81023 Theor. Math. Phys. 202, No. 1, 41-57 (2020); translation from Teor. Mat. Fiz. 202, No. 1, 47-65 (2020). MSC: 81Q10 81V10 35P05 PDF BibTeX XML Cite \textit{L. I. Danilov}, Theor. Math. Phys. 202, No. 1, 41--57 (2020; Zbl 1445.81023); translation from Teor. Mat. Fiz. 202, No. 1, 47--65 (2020) Full Text: DOI
Danilov, Leonid Ivanovich On the spectrum of a relativistic Landau Hamiltonian with a periodic electric potential. (Russian. English summary) Zbl 1452.35121 Izv. Inst. Mat. Inform., Udmurt. Gos. Univ. 54, 3-26 (2019). MSC: 35P05 35Q41 PDF BibTeX XML Cite \textit{L. I. Danilov}, Izv. Inst. Mat. Inform., Udmurt. Gos. Univ. 54, 3--26 (2019; Zbl 1452.35121) Full Text: DOI MNR
Kawamoto, Masaki Mourre theory for time-periodic magnetic fields. (English) Zbl 1433.35323 J. Funct. Anal. 277, No. 1, 1-30 (2019). MSC: 35Q41 35P25 47A40 81U05 PDF BibTeX XML Cite \textit{M. Kawamoto}, J. Funct. Anal. 277, No. 1, 1--30 (2019; Zbl 1433.35323) Full Text: DOI arXiv
Danilov, Leonid Ivanovich On the spectrum of a two-dimensional Schrödinger operator with a homogeneous magnetic field and a periodic electric potential. (Russian. English summary) Zbl 1423.35262 Izv. Inst. Mat. Inform., Udmurt. Gos. Univ. 51, 3-41 (2018). MSC: 35P05 35J10 35Q40 81Q10 PDF BibTeX XML Cite \textit{L. I. Danilov}, Izv. Inst. Mat. Inform., Udmurt. Gos. Univ. 51, 3--41 (2018; Zbl 1423.35262) Full Text: DOI MNR
Freund, Silvia; Teufel, Stefan Peierls substitution for magnetic Bloch bands. (English) Zbl 1343.81088 Anal. PDE 9, No. 4, 773-811 (2016). MSC: 81Q10 81Q05 82D20 35P05 58J53 PDF BibTeX XML Cite \textit{S. Freund} and \textit{S. Teufel}, Anal. PDE 9, No. 4, 773--811 (2016; Zbl 1343.81088) Full Text: DOI arXiv
Kjellmert, B. Electromagnetic eigenfields in checkerboard patterns. (English) Zbl 1342.78006 Numer. Methods Partial Differ. Equations 32, No. 2, 418-444 (2016). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78A25 78M30 78M22 PDF BibTeX XML Cite \textit{B. Kjellmert}, Numer. Methods Partial Differ. Equations 32, No. 2, 418--444 (2016; Zbl 1342.78006) Full Text: DOI
Luque, Alejandro; Peralta-Salas, Daniel Motion of charged particles in ABC magnetic fields. (English) Zbl 1284.34080 SIAM J. Appl. Dyn. Syst. 12, No. 4, 1889-1947 (2013). MSC: 34C60 34C20 37J30 37J40 37D45 78A35 34C23 34C28 34D20 PDF BibTeX XML Cite \textit{A. Luque} and \textit{D. Peralta-Salas}, SIAM J. Appl. Dyn. Syst. 12, No. 4, 1889--1947 (2013; Zbl 1284.34080) Full Text: DOI arXiv
Kukushkin, A. A. Homogenization of the two-dimensional periodic Dirac operator. (English. Russian original) Zbl 1285.47090 J. Math. Sci., New York 189, No. 3, 490-507 (2013); translation from Probl. Mat. Anal. 68, 141-156 (2013). Reviewer: Dian K. Palagachev (Bari) MSC: 47N20 35B27 35Q70 PDF BibTeX XML Cite \textit{A. A. Kukushkin}, J. Math. Sci., New York 189, No. 3, 490--507 (2013; Zbl 1285.47090); translation from Probl. Mat. Anal. 68, 141--156 (2013) Full Text: DOI
Cohen-Tannoudji, Claude; Diu, Bernard; Laloë, Frank Quantum mechanics. Vol. 2. Translated from the French original by Joachim v. Streubel and Jochen Balla. 4th revised ed. (Quantenmechanik. Band 2. Übersetzt aus dem Französischen von Joachim v. Streubel und Jochen Balla.) (German) Zbl 1206.81001 Berlin: de Gruyter (ISBN 978-3-11-022460-3/hbk). xiv, 657 p. (2010). Reviewer: Claudia-Veronika Meister (Darmstadt) MSC: 81-01 81Q05 81Q15 81V45 81V70 81R05 81U05 81S05 70H40 PDF BibTeX XML Cite \textit{C. Cohen-Tannoudji} et al., Quantenmechanik. Band 2. Übersetzt aus dem Französischen von Joachim v. Streubel und Jochen Balla. 4th revised ed. Berlin: de Gruyter (2010; Zbl 1206.81001)
Helffer, Bernard; Pankrashkin, Konstantin Semiclassical reduction for magnetic Schrödinger operator with periodic zero-range potentials and applications. (English) Zbl 1185.35043 Asymptotic Anal. 63, No. 1-2, 1-27 (2009). Reviewer: Nils Ackermann (México) MSC: 35J10 35P05 47G30 47N50 81Q20 PDF BibTeX XML Cite \textit{B. Helffer} and \textit{K. Pankrashkin}, Asymptotic Anal. 63, No. 1--2, 1--27 (2009; Zbl 1185.35043) Full Text: DOI arXiv
Eckstein, Andrei Unitary reduction for the two-dimensional Schrödinger operator with strong magnetic field. (English) Zbl 1121.47064 C. R., Math., Acad. Sci. Paris 344, No. 11, 715-719 (2007). MSC: 47N50 81Q10 35J10 PDF BibTeX XML Cite \textit{A. Eckstein}, C. R., Math., Acad. Sci. Paris 344, No. 11, 715--719 (2007; Zbl 1121.47064) Full Text: DOI
Cornean, Horia D.; Herbst, Ira; Skibsted, Erik Spiraling attractors and quantum dynamics for a class of long-range magnetic fields. (English) Zbl 1125.35069 J. Funct. Anal. 247, No. 1, 1-94 (2007). MSC: 35P25 35Q40 81Q10 35B41 81U05 PDF BibTeX XML Cite \textit{H. D. Cornean} et al., J. Funct. Anal. 247, No. 1, 1--94 (2007; Zbl 1125.35069) Full Text: DOI
Briet, Philippe; Cornean, Horia D.; Zagrebnov, Valentin A. Do bosons condense in a homogeneous magnetic field? (English) Zbl 1097.82002 J. Stat. Phys. 116, No. 5-6, 1545-1578 (2004). MSC: 82B10 81Q10 82D05 PDF BibTeX XML Cite \textit{P. Briet} et al., J. Stat. Phys. 116, No. 5--6, 1545--1578 (2004; Zbl 1097.82002) Full Text: DOI
Danilov, L. I. The spectrum of the two-dimensional periodic Schrödinger operator. (English) Zbl 1178.35275 Theor. Math. Phys. 134, No. 3, 392-403 (2003); translation from Teor. Mat. Fiz. 134, No. 3, 447-459 (2003). MSC: 35P05 81Q10 35J10 35Q40 PDF BibTeX XML Cite \textit{L. I. Danilov}, Theor. Math. Phys. 134, No. 3, 392--403 (2003; Zbl 1178.35275); translation from Teor. Mat. Fiz. 134, No. 3, 447--459 (2003) Full Text: DOI
Exner, P.; Němcová, K. Magnetic layers with periodic point perturbations. (English) Zbl 1058.81017 Rep. Math. Phys. 52, No. 2, 255-280 (2003). MSC: 81Q15 47B25 47N50 PDF BibTeX XML Cite \textit{P. Exner} and \textit{K. Němcová}, Rep. Math. Phys. 52, No. 2, 255--280 (2003; Zbl 1058.81017) Full Text: DOI arXiv
Suslina, T. A.; Shterenberg, R. G. Absolute continuity of the spectrum of the Schrödinger operator with the potential concentrated on a periodic system of hypersurfaces. (English. Russian original) Zbl 1068.35122 St. Petersbg. Math. J. 13, No. 5, 859-891 (2002); translation from Algebra Anal. 13, No. 5, 197-240 (2001). MSC: 35Q40 35P20 81Q10 PDF BibTeX XML Cite \textit{T. A. Suslina} and \textit{R. G. Shterenberg}, St. Petersbg. Math. J. 13, No. 5, 1 (2002; Zbl 1068.35122); translation from Algebra Anal. 13, No. 5, 197--240 (2001)
Birman, M. Sh.; Shterenberg, R. G.; Suslina, T. A. Absolute continuity of the spectrum of a two-dimensional Schrödinger operator with potential supported on a periodic system of curves. (English. Russian original) Zbl 0998.35006 St. Petersbg. Math. J. 12, No. 6, 983-1012 (2001); translation from Algebra Anal. 12, No. 6, 140-177 (2001). MSC: 35J10 35P15 35P05 PDF BibTeX XML Cite \textit{M. Sh. Birman} et al., St. Petersbg. Math. J. 12, No. 6, 983--1012 (2001; Zbl 0998.35006); translation from Algebra Anal. 12, No. 6, 140--177 (2001)
Bolotin, S. V.; Mackay, R. S. Periodic and chaotic trajectories of the second species for the \(n\)-centre problem. (English) Zbl 0979.70009 Celest. Mech. Dyn. Astron. 77, No. 1, 49-75 (2000). MSC: 70F07 78A35 PDF BibTeX XML Cite \textit{S. V. Bolotin} and \textit{R. S. Mackay}, Celest. Mech. Dyn. Astron. 77, No. 1, 49--75 (2000; Zbl 0979.70009) Full Text: DOI
Kuchment, Peter; Levendorskiǐ, Sergei On absolute continuity of spectra of periodic elliptic operators. (English) Zbl 0965.35100 Dittrich, Jaroslav (ed.) et al., Mathematical results in quantum mechanics. QMath7 conference, Prag, Czech Republic, June 22-26, 1998. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 108, 291-297 (1999). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35P05 35J10 PDF BibTeX XML Cite \textit{P. Kuchment} and \textit{S. Levendorskiǐ}, in: Mathematical results in quantum mechanics. QMath7 conference, Prag, Czech Republic, June 22--26, 1998. Basel: Birkhäuser. 291--297 (1999; Zbl 0965.35100) Full Text: arXiv
Dinaburg, E. I.; Sinai, Ya. G.; Soshnikov, A. B. Splitting of the low Landau levels into a set of positive Lebesgue measure under small periodic perturbations. (English) Zbl 0888.60055 Commun. Math. Phys. 189, No. 2, 559-575 (1997). MSC: 60H25 PDF BibTeX XML Cite \textit{E. I. Dinaburg} et al., Commun. Math. Phys. 189, No. 2, 559--575 (1997; Zbl 0888.60055) Full Text: DOI
Loginov, B. V.; Trenogin, V. A.; Vel’misov, P. A. Bifurcation and stability in some problems of continuum mechanics. (English) Zbl 0888.76031 Z. Angew. Math. Mech. 76, Suppl. 2, 241-244 (1996). MSC: 76E99 76B10 76W05 74F10 PDF BibTeX XML Cite \textit{B. V. Loginov} et al., Z. Angew. Math. Mech. 76, 241--244 (1996; Zbl 0888.76031) Full Text: DOI
Geiler, V. A.; Margulis, V. A.; Chuchaev, I. I. Spectrum structure for the three-dimensional periodic Landau operator. (English. Russian original) Zbl 0885.47016 St. Petersbg. Math. J. 8, No. 3, 447-461 (1997); translation from Algebra Anal. 8, No. 3, 104-124 (1996). MSC: 47F05 35J10 81Q05 PDF BibTeX XML Cite \textit{V. A. Geiler} et al., St. Petersbg. Math. J. 8, No. 3, 104--124 (1996; Zbl 0885.47016); translation from Algebra Anal. 8, No. 3, 104--124 (1996)
Surace, Steve A finite range operator with a quasi-periodic potential. (English) Zbl 0838.47018 Differ. Integral Equ. 9, No. 1, 213-237 (1996). MSC: 47B25 47F05 47N20 PDF BibTeX XML Cite \textit{S. Surace}, Differ. Integral Equ. 9, No. 1, 213--237 (1996; Zbl 0838.47018)
Kunz, H. Adiabatic charge transport and topological invariants for electrons in a quasi-periodic potential and a magnetic field. (English) Zbl 0823.58044 Helv. Phys. Acta 66, No. 3, 264-335 (1993). MSC: 58Z05 82B44 81Q10 81V70 82C70 PDF BibTeX XML Cite \textit{H. Kunz}, Helv. Phys. Acta 66, No. 3, 264--335 (1993; Zbl 0823.58044)
Czerwinski, M.; Brown, E. A nodal determination of the Hall conductance. (English) Zbl 0733.58046 Proc. R. Soc. Lond., Ser. A 433, No. 1889, 547-571 (1991). MSC: 58Z05 78A20 81V10 PDF BibTeX XML Cite \textit{M. Czerwinski} and \textit{E. Brown}, Proc. R. Soc. Lond., Ser. A 433, No. 1889, 547--571 (1991; Zbl 0733.58046) Full Text: DOI
Kerdelhué, P. Two dimensional Schrödinger equation with periodic potential and magnetic field. The case of triangular lattice of wells. (Equation de Schrödinger en dimension 2, avec potentiel et champ magnétique périodiques. Cas d’un réseau triangulaire de puits.) (French) Zbl 0711.35090 Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1990, No. 11, 8 p. (1990). Reviewer: B.Helffer MSC: 35P15 35J10 35S05 PDF BibTeX XML Full Text: Numdam EuDML
Helffer, B.; Sjöstrand, J. Equation de Schrödinger avec champ magnétique et équation de Harper. (The Schrödinger equation with magnetic field and the Harper equation). (French) Zbl 0699.35189 Schrödinger operators, Proc. Nord. Summer Sch. Math., Sandbjerg Slot, Sønderborg/Denmark 1988, Lect. Notes Phys. 345, 118-197 (1989). Reviewer: V.I.Ivrij MSC: 35P05 35S05 35J10 PDF BibTeX XML
Helffer, Bernard Semi-classical analysis for the Schrödinger operator and applications. (English) Zbl 0647.35002 Lecture Notes in Mathematics, 1336. Berlin etc.: Springer-Verlag. iv, 107 p. DM 23.00 (1988). Reviewer: R.Didier MSC: 35-02 35P05 35J10 81Q15 PDF BibTeX XML Cite \textit{B. Helffer}, Semi-classical analysis for the Schrödinger operator and applications. Berlin etc.: Springer-Verlag (1988; Zbl 0647.35002)
Delyon, François Absence of localisation in the almost Mathieu equation. (English) Zbl 0622.34024 J. Phys. A 20, L21-L23 (1987). MSC: 34L99 PDF BibTeX XML Cite \textit{F. Delyon}, J. Phys. A, Math. Gen. 20, L21--L23 (1987; Zbl 0622.34024) Full Text: DOI
Cycon, H. L.; Froese, R. G.; Kirsch, W.; Simon, B. Schrödinger operators, with application to quantum mechanics and global geometry. (English) Zbl 0619.47005 Springer Study edition. Texts and Monographs in Physics. Berlin etc.: Springer-Verlag. ix, 319 pp.; DM 56.00 (1987). Reviewer: M.Combescure MSC: 47A40 47B80 47-02 81U05 47A35 81U10 82B44 60H25 47A10 58J20 58J50 PDF BibTeX XML
Beyer, K. Bifurcation and stability of cellular states in magnetic fluids. (English) Zbl 0594.76106 Z. Anal. Anwend. 4, 413-428 (1985). Reviewer: P.Smith MSC: 76W05 35B32 PDF BibTeX XML Cite \textit{K. Beyer}, Z. Anal. Anwend. 4, 413--428 (1985; Zbl 0594.76106) Full Text: DOI
Avron, J.; Simon, B. Stability of gaps for periodic potentials under variation of a magnetic field. (English) Zbl 0586.35084 J. Phys. A 18, 2199-2205 (1985). MSC: 35Q99 35B10 35P15 35B37 PDF BibTeX XML Cite \textit{J. Avron} and \textit{B. Simon}, J. Phys. A, Math. Gen. 18, 2199--2205 (1985; Zbl 0586.35084) Full Text: DOI